Whats the answer if 0=0?

Question

when 0=0 does it mean no solution,undefined, or many solutions?

Answer 1

It means many solutions.

For example say you had the following system of equations:
a + 2b = 5
2a + 4b = 10

If you double the top equation and subtract you'll end up with:
0 = 0

This is a true statement so it means that any values of a and b will make the system true. There are infinitely many solutions.

If on the other hand you had:
a + b = 2
a + b = 3

This would end up with something like 2 = 3 or 0 = 1. This is a false statement so it would have no solutions.

As long as you took valid steps to get to 0 = 0, your example would be many solutions. A bad way to get there would be to multiply both sides by 0, for example. But if you are doing valid additions, subtractions and multiplies and divides by non-zero numbers, you should be okay in saying that you have many solutions.

Answer 2

infinitely many solutions:
ex.

x+y = 5
-20x -20y = -100

To cancel the x's, multiply by -20, and subtract down:
-20x -20y = -100
-20x -20y = -100

0 = 0
This means that it was the same line... therefore there are infinitely many solutions...